Edge map of an image contains a lot of information about objects in the image. That is why edge detection has been widely used in numerous image processing and vision algorithms. Although there has been a lot of research on this topic, however, most of the practically used algorithms, like a Canny edge detector, still lack basic requirement of edge localization. If noise is to be removed by using a low pass filter then edges are blurred. Contrarily, if edges have to be preserved then noise severely corrupts the edge map. In this paper, we have proposed a new method of edge detection, Difference of BiGaussian (DoBG) edge Filter, which simultaneously removes noise from real life images, while generating well localized edges. We have presented detailed analysis of our operator using 1D and 2D signals. Moreover, experimental results on published data sets show the robustness and quality of our detector.